Cooperation between firms can never improve the technical efficiency of any firm coalition. The directional distance function, by virtue of its additive nature, is a useful tool that outlines this impossibility. In this paper, the additive aggregation scheme of input/output vectors is generalized according to an aggregator. Accordingly, cooperation between firms may increase the technical efficiency of the firm group. This improvement is shown to be compatible with nonjoint semilattice technologies that bring out either output or input (weak) complementarity. Firm games are investigated to show that firms may merge on the basis of their inputs due to constraints imposed on outputs. Conversely, they may merge with respect to the outputs they can produce because of limitations imposed on inputs.